LONDON — Diageo and the family that makes Jose Cuervo tequila have agreed to swap two of their best-known brands, giving the global spirits maker a bigger presence in the tequila market.

Under the deal, Diageo will acquire full control of Don Julio, a fast-growing tequila brand, from Casa Cuervo, as well as $408 million in cash.

Cuervo, which is owned by the Beckmann family that is descended from Jose Antonio de Cuervo, will acquire Bushmills, the Irish whiskey brand.

News of the potential brand swap, expected to be completed in early 2015, surfaced over the weekend.

The deal came nearly two years after Diageo abandoned a bid to buy Cuervo outright.

Diageo, which also owns Johnnie Walker whisky, Smirnoff vodka and Captain Morgan rum, has since acquired several small brands of tequila, including Peligroso and DeLeón.

The acquisition gives Diageo greater access to a premium brand it has distributed for years.

The Don Julio brand had sales of 105 million pounds, or about $168 million, in the fiscal year ended June 30. Diageo accounted for about £75 million of those sales.

Cuervo will gain access to one of the world’s largest whiskey brands in Bushmills, which had net sales of £57 million in its fiscal year ended June 30.

As part of the deal, Cuervo will end its agreement with Diageo to produce and distribute Smirnoff in Mexico, allowing Diageo to further benefit from its soon-to-be-expanded presence there. Smirnoff had net sales in Mexico of about £9 million in its fiscal year ended June 30.

“We have secured our position in the growing super and ultra-premium segments of the tequila category and further strengthened our global footprint by expanding our leading position in Mexico, where the growth of spirits has great potential,” Ivan Menezes, the Diageo chief executive, said in a news release.